Optimal Crowdsourcing Contests

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2-approximations to conventional methods for a large family of "regular" distributions, and 4-approximations, otherwise.Comment: The paper has 17 pages and 1 figure. It is to appear in the proceedings of ACM-SIAM Symposium on Discrete Algorithms 201

Indicating Asynchronous Array Multipliers

Multiplication is an important arithmetic operation that is frequently encountered in microprocessing and digital signal processing applications, and multiplication is physically realized using a multiplier. This paper discusses the physical implementation of many indicating asynchronous array multipliers, which are inherently elastic and modular and are robust to timing, process and parametric variations. We consider the physical realization of many indicating asynchronous array multipliers using a 32/28nm CMOS technology. The weak-indication array multipliers comprise strong-indication or weak-indication full adders, and strong-indication 2-input AND functions to realize the partial products. The multipliers were synthesized in a semi-custom ASIC design style using standard library cells including a custom-designed 2-input C-element. 4x4 and 8x8 multiplication operations were considered for the physical implementations. The 4-phase return-to-zero (RTZ) and the 4-phase return-to-one (RTO) handshake protocols were utilized for data communication, and the delay-insensitive dual-rail code was used for data encoding. Among several weak-indication array multipliers, a weak-indication array multiplier utilizing a biased weak-indication full adder and the strong-indication 2-input AND function is found to have reduced cycle time and power-cycle time product with respect to RTZ and RTO handshaking for 4x4 and 8x8 multiplications. Further, the 4-phase RTO handshaking is found to be preferable to the 4-phase RTZ handshaking for achieving enhanced optimizations of the design metrics.Comment: arXiv admin note: text overlap with arXiv:1903.0943

Entwinement and the emergence of spacetime

It is conventional to study the entanglement between spatial regions of a quantum field theory. However, in some systems entanglement can be dominated by "internal", possibly gauged, degrees of freedom that are not spatially organized, and that can give rise to gaps smaller than the inverse size of the system. In a holographic context, such small gaps are associated to the appearance of horizons and singularities in the dual spacetime. Here, we propose a concept of entwinement, which is intended to capture this fine structure of the wavefunction. Holographically, entwinement probes the entanglement shadow -- the region of spacetime not probed by the minimal surfaces that compute spatial entanglement in the dual field theory. We consider the simplest example of this scenario -- a 2d conformal field theory (CFT) that is dual to a conical defect in AdS3 space. Following our previous work, we show that spatial entanglement in the CFT reproduces spacetime geometry up to a finite distance from the conical defect. We then show that the interior geometry up to the defect can be reconstructed from entwinement that is sensitive to the discretely gauged, fractionated degrees of freedom of the CFT. Entwinement in the CFT is related to non-minimal geodesics in the conical defect geometry, suggesting a potential quantum information theoretic meaning for these objects in a holographic context. These results may be relevant for the reconstruction of black hole interiors from a dual field theory.Comment: v2: Sec. 4.3 amende

The entropy of a hole in spacetime

We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a 'hole') located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.Comment: 9 pages, 1 figure; v2: published version including updated reference

The Library of Babel

We show that heavy pure states of gravity can appear to be mixed states to almost all probes. Our arguments are made for $\rm{AdS}_5$ Schwarzschild black holes using the field theory dual to string theory in such spacetimes. Our results follow from applying information theoretic notions to field theory operators capable of describing very heavy states in gravity. For certain supersymmetric states of the theory, our account is exact: the microstates are described in gravity by a spacetime ``foam'', the precise details of which are invisible to almost all probes.Comment: 7 pages, 1 figure, Essay receiving honorable mention in the 2005 Gravity Research Foundation essay competitio

Flat-space scattering and bulk locality in the AdS/CFT correspondence

The large radius limit in the AdS/CFT correspondence is expected to provide a holographic derivation of flat-space scattering amplitudes. This suggests that questions of locality in the bulk should be addressed in terms of properties of the S-matrix and their translation into the conformal field theory. There are, however, subtleties in this translation related to generic growth of amplitudes near the boundary of anti de-Sitter space. Flat space amplitudes are recovered after a delicate projection of CFT correlators onto normal-mode frequencies of AdS. Once such amplitudes are obtained from the CFT, possible criteria for approximate bulk locality include bounds on growth of amplitudes at high energies and reproduction of semiclassical gravitational scattering at long distances.Comment: 25 pages, harvmac. v2: Very minor corrections to eqs. v3: Minor improvements of discussion of locality bounds and string scattering v4. Typos fixe